A real variable characterization of Gromov hyperbolicity of flute surfaces

23 pages, 1 figure.-- MSC2000 codes: 41A10, 46E35, 46G10.-- ArXiv pre-print available at: http://arxiv.org/abs/0806.0093Previously presented as Communication at International Congress of Mathematicians 2006 (ICM2006, Madrid, Spain, Aug 22-30, 2006).Preaccepted for publication at: Osaka Journal of MathematicsIn this paper we give a characterization of the Gromov hyperbolicity of trains (a large class of Denjoy domains which contains the flute surfaces) in terms of the behavior of a real function. This function describes somehow the distances between some remarkable geodesics in the train. This theorem has several consequences; in particular, it allows to deduce a result about stability of hyperbolicity, even though the original surface and the modified one are not quasi-isometric.Research partially supported by three grants from M.E.C. (MTM 2006-11976, MTM 2006-13000-C03-02 and MTM 2007-30904-E), Spain.No publicad

Structure Theorem for Riemannian surfaces with arbitrary curvature

In this paper we prove that any Riemannian surface, with no restriction of curvature at all, can be decomposed into blocks belonging just to some of these types: generalized Y-pieces, generalized funnels and halfplanes.Comment: 15 pages, 1 latex file, 7 eps figure

The role of funnels and punctures in the Gromov hyperbolicity of Riemann surfaces

27 pages, no figures.-- MSC2000 codes: 30F20, 30F45.MR#: MR2243795 (2007e:30063)Zbl#: Zbl 1108.30031We prove results on geodesic metric spaces which guarantee that some spaces are not hyperbolic in the Gromov sense. We use these theorems in order to study the hyperbolicity of Riemann surfaces. We obtain a criterion on the genus of a surface which implies non-hyperbolicity. We also include a characterization of the hyperbolicity of a Riemann surface S* obtained by deleting a closed set from one original surface S. In the particular case when the closed set is a union of continua and isolated points, the results clarify the role of punctures and funnels (and other more general ends) in the hyperbolicity of Riemann surfaces.Research by all three authors partially supported by a grant from DGI (BFM 2003-04870), Spain. In addition, research by third author (Eva Tourís) was partially supported by a grant from DGI (BFM 2000-0022), Spain.Publicad

The Spin-Orbit Evolution of GJ 667C System: The Effect of Composition and Other Planet's Perturbations

Potentially habitable planets within the habitable zone of M-dwarfs are affected by tidal interaction. We studied the tidal evolution in GJ 667C using a numerical code we call TIDEV. We reviewed the problem of the dynamical evolution focusing on the effects that a rheological treatment, different compositions and the inclusion of orbital perturbations, have on the spin-down time and the probability to be trapped in a low spin-orbit resonance. Composition have a strong effect on the spin-down time, changing, in some cases, by almost a factor of 2 with respect to the value estimated for a reference Earth-like model. We calculated the time to reach a low resonance value (3:2) for the configuration of 6 planets. Capture probabilities are affected when assuming different compositions and eccentricities variations. We chose planets b and c to evaluate the probabilities of capture in resonances below 5:2 for two compositions: Earth-like and Waterworld planets. We found that perturbations, although having a secular effect on eccentricities, have a low impact on capture probabilities and noth- ing on spin-down times. The implications of the eccentricity variations and actual habitability of the GJ 667C system are discussed.Comment: 15 pages, 9 figures, 4 tables. Accepted for publication in MNRAS - V

Mecanismos de hidratación del yeso

There is an hypothesis that the mechanism o f gypsum hydration and dehydration is performed through two simultaneous phenomena. In this study we try to clear up this phenomenon using chlorides as accelerators or a mixture of ethanol-methanol as retarders to carry out the gypsum setting. Natural Mexican gypsum samples and a hemihydrate prepared in the laboratory are used. The following analytical techniques are used: MO, DRX, DTA, TG and DTG. In agreement with the obtained results, it can be concluded: that colloid formation depends on the action of accelerators or retarders and the crystals are a consequence of the quantity of hemihydrate formed.En el mecanismo de hidratación y deshidratación del yeso existe la hipótesis de que éste se efectúa por dos fenómenos simultáneos. Este estudio intenta esclarecer estos fenómenos, empleando: cloruros como aceleradores o mezcla etanol-metanol como retardadores para efectuar el fraguado del yeso. Se emplean muestras de yeso de origen natural mexicano y hemihydrate preparado en laboratorio; se utilizan técnicas analíticas: MO, DRX, DTA, TG y DTG. De acuerdo a los resultados obtenidos se puede deducir: que la formación del coloide depende de la acción de los agentes aceleradores o retardadores y que los cristales son consecuencia de la cantidad de hemihidrato formado

Stability of Gromov hyperbolicity

20 pages, 1 figure.-- MSC2000 codes: 30F45; 53C23, 30C99.Zbl#: Zbl pre05652685A main problem when studying any mathematical property is to determine its stability, i.e., under what type of perturbations it is preserved. With this aim, here we study the stability of Gromov hyperbolicity, a property which has been proved to be fruitful in many fields. First of all we analyze the stability under appropriate limits, in the context of general metric spaces. We also prove the stability under some transformations in Riemann surfaces, even though the original surface and the modified one are not quasi-isometric.The researches of Ana Portilla, José M. Rodríguez and Eva Tourís were partially supported by three grants from M.E.C. (MTM 2006-11976, MTM 2006-13000-C03-02 and MTM 2007-30904-E), Spain. The research of Eva Tourís was partially supported by a grant from U.C.III M./C.A.M. (CCG08-UC3M/ESP-4516), Spain.Publicad

Gromov hyperbolicity through decomposition of metrics spaces II

27 pages, no figures.-- MSC2000 codes: 30F20, 30F45.MR#: MR2030578 (2005b:30045)Zbl#: Zbl 1047.30028In this article we study the hyperbolicity in the Gromov sense of metric spaces. We deduce the hyperbolicity of a space from the hyperbolicity of its "building block components", which can be joined following an arbitrary scheme. These results are especially valuable since they simplify notably the topology and allow to obtain global results from local information. Some interesting theorems about the role of punctures and funnels on the hyperbolicity of Riemann surfaces can be deduced from the conclusions of this article.The research of the second author was partially supported by a grant from DGI (BFM 2000-0022) Spain. The research of the third author was supported by a grant from DGI (BFM 2000-0022) Spain.Publicad